Creating Inky-looking characters in Blender
If I understand correctly, your question is essentially asking how to emit smoke from a rigged and animated character.
This should work just fine, as long as the smoke modifier is after the armature modifier on the character mesh:

Example (click for a smoother video):

I found using the mesh directly as the smoke emitter provided a smoother, less lumpy result without requiring huge numbers of particles.
Smoke settings
All these settings are just stylizations on my part, they are not supposed to look like real ink in water :P
I used a fairly high resolution domain with only 1 high resolution subdivision, dissolve (though perhaps I made it dissolve a little on the fast side), and low vorticity:

For the emitter I used subframes and enabled initial velocity so that the smoke inherits the velocity of the part of the mesh it's emitted from (in the example render the smoke is actually &quot;flung&quot; by the mesh twice as fast as it technically should be, but I rather liked the effect). I also used a negative temperature difference so that the smoke drifts down over time, however I think I might have over done it a bit (the smoke falls a little fast for my taste).